A method for optimizing water resources allocation in plateau lake basins
By calculating ecological flows and establishing an optimized configuration model, combining non-cooperative game theory and dynamic adjustment mechanisms, the systematic problems of water resources management in plateau lake basins are solved, and the sustainable utilization and ecological protection of water resources are achieved.
Patent Information
- Application Number
- CN202411854184.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-16
- Publication Date
- 2025-04-01
AI Technical Summary
Plateau lake basins are facing problems such as water shortage, intensified water pollution, and ecological degradation. Traditional water resource management methods lack systematicity and are difficult to cope with the impact of complex and changing hydrological conditions and human activities.
By accurately calculating ecological flow, establishing an optimized configuration model, applying non-cooperative game theory, achieving multi-objective optimization, introducing dynamic adjustment and feedback mechanisms, providing a scientific and dynamic water resource optimization allocation method.
It has achieved sustainable use and ecological protection of water resources, met the needs of economic and social development, improved the scientificity and effectiveness of water resources management, and reduced the risk of water resources conflicts.
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Figure CN119740825A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of water resource management, and more specifically to a method for optimizing the allocation of water resources in a plateau lake basin. Background Art
[0002] As an important freshwater resource reservoir, plateau lakes are of great significance for maintaining ecological balance, ensuring regional water security and promoting local economic development. However, with the impact of climate change and human activities, plateau lake basins are facing a series of problems such as water shortage, increased water pollution and ecological degradation. These problems not only affect the ecological health of the lakes, but also bring challenges to the supply and utilization of water resources in surrounding areas.
[0003] Traditional water resource management methods for plateau lake basins often lack systematicity and are difficult to cope with the complex and changing hydrological conditions and the impact of human activities. In addition, due to the special geographical and climatic conditions of the plateau area, conventional water resource allocation methods may not be applicable to plateau lake basins, and it is necessary to develop water resource optimization allocation methods that are more suitable for plateau characteristics.
[0004] At present, the main problems in water resource allocation in plateau lake basins are as follows:
[0005] Inaccurate water resource assessment: The lack of a comprehensive and accurate assessment of the water resource status of plateau lake basins has resulted in a lack of scientific basis for water resource allocation plans.
[0006] Low efficiency of water resource utilization: The efficiency of water resource utilization in plateau lake basins is generally low, and there is a waste of water resources.
[0007] Conflict between ecological protection and water resource development: In the process of water resource development and utilization, the protection of plateau lake ecosystems is often neglected, leading to ecological degradation.
[0008] Weak ability to cope with climate change: Against the backdrop of global climate change, water resource allocation methods in plateau lake basins have failed to effectively cope with the impacts of climate variability.
[0009] Therefore, it is necessary to develop a new method for optimizing the allocation of water resources in plateau lake basins, which can comprehensively consider the particularities of plateau lake basins and achieve the dual goals of efficient utilization of water resources and ecological protection.
[0010] There have been some studies and practices on water resource optimization allocation at home and abroad, for example, by establishing hydrological models to predict the changing trend of water resources, using multi-objective optimization algorithms to balance the water resource needs of different stakeholders, and adopting ecological flow guarantee measures to protect the water ecological environment. However, the applicability of these methods in plateau lake basins still needs to be improved, especially in terms of climate change adaptation and ecological protection.
[0011] Therefore, how to provide a method for optimizing water resource allocation that is adapted to the characteristics of plateau lake basins is an urgent problem that technicians in this field need to solve. Summary of the invention
[0012] In view of this, the present invention provides a method for optimizing the allocation of water resources in plateau lake basins. By accurately calculating ecological flow, establishing an optimization allocation model, applying non-cooperative game theory, realizing multi-objective optimization, and introducing dynamic adjustment and feedback mechanisms, a scientific and dynamic method for optimizing the allocation of water resources is provided for plateau lake basins, so as to achieve sustainable utilization of water resources and ecological protection, while meeting the needs of economic and social development.
[0013] In order to achieve the above object, the present invention adopts the following technical solution:
[0014] The present invention provides a method for optimizing water resource allocation in a plateau lake basin, comprising:
[0015] Obtaining ecological data of plateau lake basins and calculating ecological flows based on said ecological data;
[0016] Establishing a water resource optimization allocation model based on the ecological flow, water resource demanders and water resource suppliers;
[0017] Based on the water resources optimization allocation model and the non-cooperative game decision-making method, a water resources optimization allocation non-cooperative game decision-making model is constructed;
[0018] The improved NSGA-Ⅲ genetic algorithm is used to solve the non-cooperative game decision-making model and obtain the optimal solution of the water resources optimization allocation model.
[0019] Preferably, obtaining ecological data of plateau lake basins and calculating ecological flow based on the ecological data includes:
[0020] Obtaining ecological data of plateau lake basins, the ecological data including: hydrological data, ecological data, environmental data, meteorological data, and geological data;
[0021] The dominant factors of the plateau lake basin size are selected according to the environmental data, hydrological data and ecological data, and the ecological water demand is calculated by any one of the hydrological method, hydraulic method or habitat simulation method according to the determination of the dominant factors;
[0022] Determine the water consumption factor of the plateau lake basin according to the meteorological data and the geological data, and calculate the water consumption of each water consumption factor based on the meteorological data and the geological data;
[0023] The ecological water demand and the water consumption of each water consumption factor are added together to obtain the ecological flow of the plateau lake basin.
[0024] Preferably, a water resource optimization allocation model is established based on the ecological flow, water resource demand tasks and water resource supply, including:
[0025] The structure includes n water demanders A = {A1, A2, ..., An}, m ecological flows B = {B1, B2, ..., Bm}, and m water supplyers C = {C1, C2, ..., Cm};
[0026] A supply relationship between the water resource demander and the water resource supplier is established based on the ecological flow, and the constraints of the supply relationship include:
[0027] Supply constraints: Among them, x i,j represents the amount of water supplied by the jth water resource supplier to the ith water resource demander, C j is the water supply capacity of the jth water resource supplier, B j is the ecological flow of the jth water resource supplier;
[0028] Requirements constraints: Among them, A i is the water demand of the ith water resource demander.
[0029] Preferably, based on the water resources optimal allocation model and the non-cooperative game decision-making method, a water resources optimal allocation non-cooperative game decision-making model is constructed, including:
[0030] The concept of non-cooperative game is introduced into the water resource optimization allocation model, and water supply resource demand index and water resource supply index are considered. The indexes include: water resource cost, water supply, water price and water cost;
[0031] Normalize each index to obtain a normalized form;
[0032] A non-cooperative game decision model for optimal allocation of water resources is established based on a non-cooperative game decision method. The objective function of the non-cooperative game decision model for optimal allocation of water resources includes taking different water resource demand parties as game parties, and taking the multi-objective optimization function of the water supply resource demand index and the water resource supply index as the profit function of the two game parties, thereby obtaining a non-cooperative game decision model for optimal allocation of water resources.
[0033] Preferably, the non-cooperative game decision model for optimal allocation of water resources is:
[0034]
[0035] Among them, y S is the benefit of water resource supplier; i is the water price supplied to the i-th water demander; x iis the amount of water provided by the water resource supplier to the water resource demander i; S is the unit water supply cost of the water resource supplier; n is the total number of water resource demanders; y D is the benefit to the water demander; W i is the amount of water allocated to the i-th water demander, P i is the water price supplied to the i-th water demander, Y i is the output of the i-th water demander as a function of water quantity, C i is the water cost of the ith water demander, and α, β, γ are weight coefficients.
[0036] Preferably, an improved NSGA-III genetic algorithm is used to solve the non-cooperative game decision model to obtain the optimal solution of the water resources optimization allocation model, including:
[0037] After initialization parameter setting and decoding, the parent generation water resource configuration combination is genetically manipulated to generate the child generation water resource configuration combination;
[0038] The parent water resource configuration combination and the child water resource configuration combination are merged and then fast non-dominated sorting is performed. Each individual of the target water resource configuration combination is mapped to the normalized hyperplane where the reference point is located, and an association operation is performed with the generated reference point to generate a water resource configuration combination population.
[0039] The evolutionary stage of the water resource configuration combination population is judged according to the rate of change of population entropy value. The improved NSGA-Ⅲ genetic algorithm and Nash equilibrium strategy are combined through adaptive elimination strategy to prune and merge the water resource configuration combination population. The pruned and merged water resource configuration combination is used as the parent water resource configuration combination of the next iteration to judge whether the number of iterations is greater than the maximum number of iterations. If it is greater than the maximum number of iterations, the Pareto optimal solution set is output and the algorithm ends. If not, it jumps to the parent water resource configuration combination gene operation to generate the child water resource configuration combination process and continues to run.
[0040] Preferably, the method further comprises: applying the configuration scheme to the plateau lake basin, obtaining the actual water demand, calculating the deviation between the configured water volume and the actual water demand, and obtaining a configuration deviation sequence;
[0041] Constructing a feedback gain function and obtaining a gain using the deviation sequence;
[0042] The gain is used to adjust the configuration scheme for the future period to obtain a feedback configuration scheme.
[0043] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for optimizing the allocation of water resources in plateau lake basins. By collecting hydrological, ecological, environmental, meteorological and geological data, the ecological flow is accurately calculated to ensure the health of the lake ecosystem. The established optimization allocation model takes into account the relationship between water resource supply and demand and ecological protection needs, introduces non-cooperative game theory, and realizes fair and effective water resource allocation through multi-objective optimization. The improved NSGA-Ⅲ genetic algorithm is used to solve the non-cooperative game decision model to find the Pareto optimal solution that satisfies the interests of multiple parties and maximizes the economic benefits of water resource suppliers and demanders. The dynamic adjustment and feedback mechanism enables the configuration plan to adapt to changes in actual water demand and enhance the adaptability and robustness of the system. The implementation of the present invention helps to improve the scientificity and effectiveness of water resource management, promote the sustainable development of plateau lake basins, reduce the risk of water resource conflicts, and provide decision support for policy making. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.
[0045] Figure 1 The present invention provides a flow chart of a method for optimizing water resources allocation in a plateau lake basin. DETAILED DESCRIPTION
[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0047] The embodiment of the present invention discloses a method for optimizing water resources allocation in a plateau lake basin. Figure 1 As shown, including:
[0048] Obtain ecological data of plateau lake basins and calculate ecological flows based on the ecological data;
[0049] A water resource optimization allocation model is established based on ecological flow, water resource demanders and water resource suppliers; water resource demanders include agricultural irrigation, industrial water, domestic water, etc., and water resource suppliers are water sources in the plateau lake basin. This model not only takes into account the supply and demand relationship of water resources, but also fully considers the needs of ecological protection, ensuring that the water resource allocation plan not only meets the needs of human activities, but also does not damage the ecological environment of the lake basin.
[0050] Based on the water resources optimization allocation model and non-cooperative game decision-making method, a non-cooperative game decision-making model for water resources optimization allocation is constructed; this model takes water resources demanders and suppliers as participants in the game, and by simulating the strategic choices and interactions of all parties in water resources allocation, it seeks the optimal water resources allocation plan to maximize the interests of all parties.
[0051] The improved NSGA-Ⅲ genetic algorithm is used to solve the non-cooperative game decision model and obtain the optimal solution of the water resources optimization allocation model. NSGA-Ⅲ is a multi-objective optimization algorithm that can quickly converge to the optimal solution while ensuring the diversity of solutions.
[0052] Specifically, the ecological data of plateau lake basins are obtained and the ecological flow is calculated based on the ecological data, including:
[0053] Obtain ecological data of plateau lake basins. Ecological data include: hydrological data, ecological data, environmental data, meteorological data, and geological data. Hydrological data include lake water level changes, runoff, flow rate, water balance, etc., which are used to reflect the hydrological cycle and water dynamics of the lake. Ecological data include aquatic species, quantity, distribution, wetland vegetation type, coverage, and soil biological community, etc., which are used to reveal the structure and function of the lake ecosystem. Environmental data include lake water quality parameters (such as dissolved oxygen, pH value, nutrient concentration, heavy metal content, etc.), as well as land use types and human activity intensity around the lake, which are used to reflect the quality of the lake and its surrounding environment. Meteorological data include rainfall, evaporation, temperature, wind speed, etc., which are used to assess the water balance of the lake and the impact of climate. Geological data include the geological structure, soil type, groundwater distribution, etc. of the lake basin, which are used to assess the water supply and groundwater dynamics of the lake.
[0054] The dominant factors affecting the size of plateau lake basins are screened based on environmental data, hydrological data, and ecological data. Based on the determination of the dominant factors, hydrological methods, hydraulic methods, or habitat simulation methods are used to calculate ecological water demand. Statistical analysis, machine learning, or expert judgment are used to screen out the dominant factors affecting the size of plateau lake basins, including lake area, aquatic biodiversity, etc.
[0055] The water consumption factors of the plateau lake basin are determined based on meteorological and geological data, and the water consumption of each water consumption factor is calculated based on the meteorological and geological data; the water consumption factors include evapotranspiration, infiltration, greening and soil water replenishment, and landscape water replacement consumption.
[0056] The ecological water demand and the water consumption of each water consumption factor are added together to obtain the ecological flow of the plateau lake basin.
[0057] Specifically, a water resources optimization allocation model is established based on ecological flow, water resources demand tasks and water resources supply, including:
[0058] The structure includes n water demanders A = {A1, A2, ..., An}, m ecological flows B = {B1, B2, ..., Bm}, and m water supplyers C = {C1, C2, ..., Cm};
[0059] The supply relationship between water demanders and water suppliers is constructed based on ecological flow. The constraints of the supply relationship include:
[0060] Supply constraints: Among them, x i,j represents the amount of water supplied by the jth water resource supplier to the ith water resource demander, C j is the water supply capacity of the jth water resource supplier, B j is the ecological flow of the jth water resource supplier;
[0061] Requirements constraints: Among them, A i is the water demand of the ith water resource demander.
[0062] Furthermore, based on the water resources optimal allocation model and the non-cooperative game decision-making method, a non-cooperative game decision-making model for water resources optimal allocation is constructed, including:
[0063] The concept of non-cooperative game is introduced into the water resources optimization allocation model, and water supply resource demand indicators and water resources supply indicators are considered. The indicators include: water resource cost, water supply, water price, and water cost;
[0064] Normalize each index to obtain a normalized form;
[0065] Based on the non-cooperative game decision-making method, a non-cooperative game decision-making model for optimal allocation of water resources is established. The objective function of the non-cooperative game decision-making model for optimal allocation of water resources includes taking different water resource demand parties as game parties, and taking the multi-objective optimization function of water supply resource demand indicators and water resource supply indicators as the profit function of the two game parties, thus obtaining the non-cooperative game decision-making model for optimal allocation of water resources.
[0066] Furthermore, the non-cooperative game decision model for optimal allocation of water resources is:
[0067]
[0068] Among them, y S is the benefit of water resource supplier; i is the water price supplied to the i-th water demander; x i is the amount of water provided by the water resource supplier to the water resource demander i; S is the unit water supply cost of the water resource supplier; n is the total number of water resource demanders; y D is the benefit to the water demander; W i is the amount of water allocated to the i-th water demander, P i is the water price supplied to the i-th water demander, Y i is the output of the i-th water demander as a function of water quantity, C i is the water cost of the ith water demander, and α, β, γ are weight coefficients.
[0069] In another embodiment, an improved NSGA-III genetic algorithm is used to solve the non-cooperative game decision model to obtain the optimal solution of the water resources optimization allocation model, including:
[0070] After initialization parameter setting and decoding, the parent generation water resource configuration combination is genetically manipulated to generate the child generation water resource configuration combination;
[0071] The parent water resource configuration combination and the child water resource configuration combination are merged and then fast non-dominated sorting is performed. Each individual of the target water resource configuration combination is mapped to the normalized hyperplane where the reference point is located, and an association operation is performed with the generated reference point to generate a water resource configuration combination population.
[0072] The evolutionary stage of the water resource configuration combination population is judged according to the rate of change of population entropy value. The improved NSGA-Ⅲ genetic algorithm and Nash equilibrium strategy are combined through adaptive elimination strategy to prune and merge the water resource configuration combination population. The pruned and merged water resource configuration combination is used as the parent water resource configuration combination of the next iteration to judge whether the number of iterations is greater than the maximum number of iterations. If it is greater than the maximum number of iterations, the Pareto optimal solution set is output and the algorithm ends. If not, it jumps to the parent water resource configuration combination gene operation to generate the child water resource configuration combination process and continues to run.
[0073] In another embodiment, the method provided by the present invention further includes: applying the configuration scheme to a plateau lake basin, obtaining actual water demand, calculating the deviation between the configured water volume and the actual water demand, and obtaining a configuration deviation sequence; the configuration deviation calculation formula is:
[0074] P(t)=I(t)-R(t)
[0075] Among them, P(t) is the deviation sequence at time t, I(t) is the configuration plan at time t, and R(t) is the actual water resource demand at time t.
[0076] Construct a feedback gain function and use the deviation sequence to get the gain; the feedback gain function is:
[0077] G(t)=Kr*P(t)+Kd*∈
[0078] Among them, G(t) is the gain, Kr is the error coefficient, ∈ is the noise disturbance, and Kd is the noise disturbance coefficient. According to the above formula, the error information is fed back to the gain at a certain ratio. At the same time, the feedback gain is a random variable disturbed by noise. Drawing on the design of the gain function in the Kalman filter theory, the noise disturbance is designed to be a random variable that obeys the Gaussian distribution.
[0079] The gain is used to adjust the configuration plan for the future period to obtain the feedback configuration plan. The feedback configuration adjustment plan is:
[0080] F0(t+1)=I(t+1)+G(t)
[0081] Where, F(t+1) is the feedback configuration adjustment scheme at time t+1;
[0082] Then, according to the resource configuration constraints, the feedback configuration adjustment plan is further adjusted to obtain the final feedback configuration plan. The adjustment equation is:
[0083] F1(t+1)=mid{Min(d), F0(t+1), Max(d)}
[0084] Where mid is the middle value function, Min(d) and Max(d) are the defined minimum and maximum values of the dispensable water;
[0085] Finally, the configuration scheme is adjusted moment by moment to obtain a feedback configuration scheme.
[0086] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.
[0087] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for optimizing water resources allocation in plateau lake basins, characterized in that: include: Obtaining ecological data of plateau lake basins and calculating ecological flows based on said ecological data; Establishing a water resource optimization allocation model based on the ecological flow, water resource demanders and water resource suppliers; Based on the water resources optimization allocation model and the non-cooperative game decision-making method, a water resources optimization allocation non-cooperative game decision-making model is constructed; The improved NSGA-Ⅲ genetic algorithm is used to solve the non-cooperative game decision-making model and obtain the optimal solution of the water resources optimization allocation model.
2. A method for optimizing water resources allocation in plateau lake basins according to claim 1, characterized in that: Obtain ecological data of plateau lake basins and calculate ecological flows based on the ecological data, including: Obtaining ecological data of plateau lake basins, the ecological data including: hydrological data, ecological data, environmental data, meteorological data, and geological data; The dominant factors of the plateau lake basin size are selected according to the environmental data, hydrological data and ecological data, and the ecological water demand is calculated by using any one of the hydrological method, hydraulic method or habitat simulation method according to the determination of the dominant factors; Determine the water consumption factor of the plateau lake basin according to the meteorological data and the geological data, and calculate the water consumption of each water consumption factor based on the meteorological data and the geological data; The ecological water demand and the water consumption of each water consumption factor are added together to obtain the ecological flow of the plateau lake basin.
3. The method for optimizing water resources allocation in plateau lake basins according to claim 1 is characterized in that: A water resource optimization allocation model is established based on the ecological flow, water resource demand tasks and water resource supply, including: The structure includes n water demanders A = {A1, A2, ..., An}, m ecological flows B = {B1, B2, ..., Bm}, and m water supplyers C = {C1, C2, ..., Cm}; A supply relationship between the water resource demander and the water resource supplier is established based on the ecological flow, and the constraints of the supply relationship include: Supply constraints: Among them, x i,j represents the amount of water supplied by the jth water resource supplier to the ith water resource demander, C j is the water supply capacity of the jth water resource supplier, B j is the ecological flow of the jth water resource supplier; Requirements constraints: Among them, A i is the water demand of the ith water resource demander.
4. The method for optimizing water resources allocation in plateau lake basins according to claim 1 is characterized in that: Based on the water resources optimization allocation model and the non-cooperative game decision-making method, a water resources optimization allocation non-cooperative game decision-making model is constructed, including: The concept of non-cooperative game is introduced into the water resource optimization allocation model, and water supply resource demand index and water resource supply index are considered. The indexes include: water resource cost, water supply, water price and water cost; Normalize each index to obtain a normalized form; A non-cooperative game decision model for optimal allocation of water resources is established based on a non-cooperative game decision method. The objective function of the non-cooperative game decision model for optimal allocation of water resources includes taking different water resource demand parties as game parties, and taking the multi-objective optimization function of the water supply resource demand index and the water resource supply index as the profit function of the two game parties, thereby obtaining a non-cooperative game decision model for optimal allocation of water resources.
5. A method for optimizing water resources allocation in plateau lake basins according to claim 4, characterized in that: The non-cooperative game decision model for optimal allocation of water resources is: Among them, y S is the benefit of water resource supplier; i is the water price supplied to the i-th water demander; x i is the amount of water provided by the water resource supplier to the water resource demander i; S is the unit water supply cost of the water resource supplier; n is the total number of water resource demanders; y D is the benefit of water demanders; W i is the amount of water allocated to the i-th water demander, P i is the water price supplied to the i-th water demander, Y i is the output of the i-th water demander as a function of water quantity, C i is the water cost of the ith water demander, and α, β, γ are weight coefficients.
6. The method for optimizing water resources allocation in plateau lake basins according to claim 1 is characterized in that: The improved NSGA-Ⅲ genetic algorithm is used to solve the non-cooperative game decision model and obtain the optimal solution of the water resources optimization allocation model, including: After initialization parameter setting and decoding, the parent generation water resource configuration combination is genetically manipulated to generate the child generation water resource configuration combination; The parent water resource configuration combination and the child water resource configuration combination are merged and then fast non-dominated sorting is performed. Each individual of the target water resource configuration combination is mapped to the normalized hyperplane where the reference point is located, and an association operation is performed with the generated reference point to generate a water resource configuration combination population. The evolutionary stage of the water resource configuration combination population is judged according to the rate of change of population entropy value. The improved NSGA-Ⅲ genetic algorithm and Nash equilibrium strategy are combined through adaptive elimination strategy to prune and merge the water resource configuration combination population. The pruned and merged water resource configuration combination is used as the parent water resource configuration combination of the next iteration to judge whether the number of iterations is greater than the maximum number of iterations. If it is greater than the maximum number of iterations, the Pareto optimal solution set is output and the algorithm ends. If not, it jumps to the parent water resource configuration combination gene operation to generate the child water resource configuration combination process and continues to run.
7. The method for optimizing water resources allocation in plateau lake basins according to claim 1 is characterized in that: The method further comprises: applying the configuration scheme to the plateau lake basin, obtaining actual water demand, calculating the deviation between the configured water volume and the actual water demand, and obtaining a configuration deviation sequence; Constructing a feedback gain function and obtaining a gain using the deviation sequence; The gain is used to adjust the configuration scheme for the future period to obtain a feedback configuration scheme.